The CW has two huge super hero stars in The Flash and Arrow, now CBS is getting their own in Supergirl. A lot of people are rooting for them to crossover, and rumors are surfacing they might. But here is the main reason The Flash and Arrow shouldn't crossover with Supergirl.
Gee Nathan, what does Superman have to do with any of this? Well Nathan, in the Supergirl trailer they already mentioned Superman countless times. And you can't just mention Superman countless time and expect fans not to expect him. If they are developing a TV Justice League I'm in, but don't wave it in our faces then take it away.